Broad band microwave phase shifter



Oct. 11, 1960 2,956,247

P. J. SFERRAZZA BROAD BAND MICROWAVE PHASE SHIFTER Filed Jan.' 2e. 195eUnited States Patent 1 Eice Patented Oct. 1l, 1960 BROAD BAND MICROWAVEPHASE SHIFIER Peter I. Sferram, Wantagh, N.Y., :signor to Sperry RandCorporation, a corporation nl Delaware Filed 1.11.26, 195s, sa. No.561,401

s Chim. (cl. asa-s1) This invention relates generally to microwave phaseshifting devices, and more particularly, is concerned with a structurefor introducing a substantially fixed predetermined phase shift along awave transmission line over a broad frequency band.

It is frequently desirable in microwave transmission systems tointroduce a fixed amount of phase shift into one transmission path, forexample, to change the phase relative to a signal transmitted by secondtransmission path. One rather simple and straightforward way ofaccomplishing this Iresult is by making one transmission path longerthan the other by a -action of a wavelength .corresponding to thedesired phase shift. Such a scheme,

however, is highly frequency sensitive since any change in wavelengthchanges the relative phase of energy transmitted by the two paths.

Other arrangements for introducing a fixed phase shift include theintroduction in one wave guide transmission path of a dielectric insertwhich effectively changes the wavelength of the energy transmitted inthe region of the dielectric. It can be shown that by proper taperingvor stepping of the dielectric insert, the frequency over which a givenphase shift is achieved can be extended. However, the insertion ofdielectric within the wave guide has the objection that it substantiallyreduces the power handling capacity of the transmission line in that thedielectric -absorbs energy to a degree, which in the presence of highincident energy, results in overheating of the dielectn'c.

Yet anotherarrangement heretofore proposed for introducing phase shiftinto a wave guide transmission line has been to use filter sectionsincorporating reactive elements such as irises and probes. The 4reactiveelements of the filter sections introduced into the wave guidetransmission iline greatly reduce the power handling capacity of thetransmission line by rincreasing the probability of voltage breakdown. v

It is the general object of this invention to avoid and overcome theforegoing and other diiculties in and objections to the prior artpractices by the provision of a microwave phase shifter which provides asubstantially constant phase shift over an extended frequency band yetdoes not materially reduce the power handling capacity of the associatedwave guide transmission line.

Another object of this invention is the provision of a phase shifterthat introduces negligible reflection without special matchingconnection means.

These objects and other objects are achieved according to the presentinvention by providing a guided path for microwave energy, the pathbeing bonded by conducting surfaces into one of which are insertedbranch microwave transmission devices. The branch devices aredimensioned and terminated so as to produce a coeicient of coupling withrespect to the guided path whereby a corresponding predetermined phaseshift is introduced into the microwave energy yflowing in` the guidedpath. In a typical embodiment of the present invention, there isprovided a plurality of rectangular wave guide shorted stubsectionseoupled toa broad wall of a main rectangular wave guide section,theA stub sections being series connected to the lmain wave guidesection. lThe stub sections are an eighth wavelength long at the designfrequency as measured from the broad wall of the associated main waveguide to the shorted end of the stub section. Adjacent stub sections arespaced from each other along the wave guide la center-to-center distanceof a quarter wavelength at the design frequency.

For a better understanding of the invention, reference should be had tothe accompanying drawings, wherein:

Fig. 1 is a perspective view of one embodiment of the present invention;

Fig. 2 is a schematic showing of a branched-guide coupler useful inexplaining the operation of the present invention;

Fig. 2a is a vector diagram of the voltages in Fig. 2;

Fig. 3 is a schematic diagram of the embodiment of the present inventionshown in-Fig. l;

Fig. 3a is a vector diagram of the voltages in Fig. 3;

Fig. 4 is a graph useful in explaining the design characteristics of thephase shifter; and

Fig. 5 is a schematic showing of a modification of the phase shifter ofFig. l.

In the embodiment of the invention as shown in Fig. 1, the numeral 10indicates generally a section of rectangular wave guide for couplingenergy, for example, from a microwave source 12 to a load 14. A xedphase shift is introduced along the length of rectangular wave guide 10by a pair of shorted wave guide stub sections 16 and 18. These shortedstub sections are joined at one end to a broad wall of the rectangularwave guide section 10, forming E-plane or series type T junctions withthe wave guide 10. The center spacing between adjacent stubs 16 and 18is electrically a quarter wavelength at the design frequency of thephase shifter, while the length of the shorted stub sections iselectrically an eighth wavelength from the shorted end to the end joinedto the broad wall of the wave guide section 10. The narrow dimension ofthe rectangular wave guide stub sections 16 and 18 (the dimensionextending parallel to the longitudinal axis of the wave guide section10) is established according to the degree of phase shift desired, aswill hereinafter be explained.

Operation of the phase shifter of Fig. 1 can best be understood byreference to the operation of the wellv known branched-guide directionalcoupler, as shown schematically in Fig. 2. The theory of operation ofthe branched-guide coupler has been extensively analyzed heretofore.See, for example, vol. ll, Radiation Laboratory Series, McGraw-Hill BookCompany, page 866. The branched-guide coupler, -as shown in Fig. 2,includes a pair of rectangular wave guide sections 20 and 22, formingarms 1, 2, 3, and 4 of the coupler, and two'coupling stub sections 24and 26, the stub sections being a quarter wavelength long and spacedapart -a quarter wavelength. lf a voltage E1 at an assigned zero phaseangle is fed into arm 1 of the directional coupler, part of the energywill be coupled down the same wave guide section 20 to arm 2 and part ofthe energy will be coupled in one direction in the wave guide 22 to arm3. Due to the directivity characteristic of the coupler no energy iscoupled to arm 4. Such a directional coupler has an input impedance,coupling, and directivity that are substantially independent offrequency to a first order approximation, as analyzed in the aboveidentified publication.

As is characteristic of directional couplers of high directivity, theenergy coupled into the wave guide section 22 and out arm 3 is shiftedby substantially 90 from the energy coupled directly down the wave guidesection 20 and out arm 2. 'Ihe relative magnitude of the two outputvoltages from arm 2 and arm 3 of the relative phase angle of -90.

directional coupler Adepends upon the 'amount of coupling between thetwo wave guide sections 20 and 22. Thus the energy out of arm 3 in thewave guide section 22 hasa magnitude CE1 at a relative phase angle of 90as compared to the input wave (neglecting phase change due topropagation path length) where c is the coupling coeicient determined bythe degree of coupling provided by the stub sections 24 and 26. Thecoupling coefficient varies between zero and unity and can be controlledby changing the narrow dimension of the stub sections 24 and 26. Theenergy out of arm 2 of the coupler accordingly has a magnitude of\/lc2E1 at a relative phase angle of as compared to the input wave.

Now consider a second input voltage E2, having an assigned zero phaseangle so as to be in phase with the input voltage E1 fed into arm 4.Part of the energy will be coupled directly down the wave guide section22 with a magnitude of \/1c2E2 while the other portion 4will be coupledout of arm 2 with a magnitude of cli.n at a The resultant output fromarm 2 of the directional coupler therefore is the sum of the twovoltages \/l-c2E1 and CE, having a phase quadrature relationship, asshown by the vector diagram of Fig. 2a. It will be readily apparent fromFig. 2a that the phase angle 0 of the resultant voltage depends on therelative magnitude of the two voltages E1 and E, and the value of thecoupling coeflcient c.

If it is assumed that E1 and E, are equal, a voltage null exists in thestub sections 24 and 26 at a point halfway between the ends of the stubsections. This can be seen qualitatively by the vector arrowsrepresenting the voltages El and E, in Fig. 2. At the center of the stubsections 24 and 26, the two voltages produced by E1 and E2 are equal inmagnitude and 180 out of phase so that complete cancellation takesplace. Thus, a short circuit may be introduced in the st-ub sections attheir midpoint, as indicated by the broken line 28, without any apparentchange in the output ofvarms 2 and 3. The resulting structure with thetop portion removed is shown in Fig. 3, which it will be seen is aschematic showing of the phase shifter of the present invention,described in connection with Fig. l.

Itis evident by comparing lthe structure of Fig. 3 with Fig. 2 asdescribed above that an output voltage is provided by the phase shifterof Fig. l having two components whose relative amplitudes areproportional to the input voltage where the respective proportionalityfactors are \/1c2 and c. These two components have a 90 phaserelationship. The vector diagram of Fig. 3a shows that the resultantoutput voltage is equal in magnitude to the input voltage but varies inrelative phase through an angle 0 to 90 depending upon the value of thecoupling coelicient c, which in turn is determined by the narrowdimensions of the wave guide stubs, as described above.

The narrow dimensions of the branch wave guides in the structure of Fig.1 can be determined by the following equations:

In the above equations, 0 is the phase shift introduced by the phaseshifter, c is the coupling coetlcient of the equivalent branch guidecoupler, C is the coupling in db provided by the T junctions, Z is theimpedance of the branch guide or stub normalized to the impedance of themain wave guide transmission line, and b and b' are the narrowcross-sectional dimensions of the main and branch wave guidesrespectively, as indicated in Fig. 3. Equation 3 is plotted in Fig. 4.When using Equation 4, the value of nz (a correction factor forfrequency) is determined from the frequency correction curves given invol. l0, Radiation Laboratory Series, McGraw-Hill Book Company, page346. At cut-off n2 is equal to one.

For example, assume that the main wave, guide is 1 x 2" operating a't adesign wavelength of 2.5 inches and a phase [shift of 45 is desired. BryEquation 1, c would be equal to .707. From Equation 2, C would then be-3 db. From the curve of Fig. 4, Z would then be .75, and therefore b',uncorrected for frequency would be 0.75". Corrected for frequency, thevalue of b would be about 0.9".

It should be noted that if b' exceeds b, the coupling, according to thecurve of Fig. 4, begins to drop olf. As apractical matter therefore thestub wave guides are always smaller than the main wave guide, and iflarger phase shifts are desired than can be obtained by two stubs withlimited coupling, additional pairs of stub wave guides are provided.

While the phase shift introduced by the double stub device of Fig. 1 hasthe same broad band frequency response characteristics of thebranched-guide coupler, the frequency band can be even further extendedby providing additional stub. sections, as shown in Fig. 5. Again thestub sections are an eighth wavelength long at the design frequency fromthe short circuit end to the end joined to the broad wall of the mainwave guide section, and the stub sections are spaced at center-tocenterdistance of a quarter wavelength. However, to improve the frequencycharacteristics of the phase shifter, the narrow dimensions of the waveguide stubs are varied according to Iwell known broad-bandingtechniques. Ihe narrow dimensions of the stub wave guides can beproportioned, for example, so that the amplitude of coupling bytherespective stub wave guides varies according to the coecients of abinomial expansion or the well known Tchebyschetf polynomial expansion,in the same manner as has been heretofore taught in connection withmultiple-hole broad band directional couplers.

'Ihe coefficients of a binomial expansion are given in the followingtable:

Number of stubs N- and for the Tchebyschel polynomial are given in thefollowing ltable for p=2, where p is the ratio of the guide wavelengthsat the edges of the operating frequency band.

Relative amplitude a 'Ihe relation between the coupling coecient c1 forthe smallest pair of stubs having equal coupling and the couplingcoeflicient c of all the stubs may be expressed by the equation If thequantity in the brackets of Equation 5 is small, Equation 5 can berewritten as The coupling of any other pair is then found from theexpression C,= C, +20 10g (s) The size of the narrow dimension 6' of thestub wave guides can then be determined as before from the graph of Fig.4. If there are an odd number of stubs, calculations are made in thesame way except the center stub is considered as one element of a pair.

From the above description it will be seen that the various objects ofthe invention have been achieved in one embodiment by providing meansfor introducing a predetermined phase shift iuto a rectangular waveguide transmission line. 'Ihe phase shifter, utilizing stubs that are aneighth wavelength long and spaced a quarter wavelength apart, has thesame broad band properties as the phase shifter comprising a mainrectangular wave guide transmission line, a plurality of rectangularwave guide shorted stub sections each joined at one end to the broadwall of the main waveguide in a series T junction, the stub sectionsbeing substantially an eighth wavelength long at the design frequency asmeasured from the junction end to the shorted end, and adjacent stubsections being spaced from each other along the main wave guide acenter-tocenter distance of substantially a quarter wavelength at thedesign frequency, the stub sections being dimensioned so as to produce atotal coupling coefficient c related to the desired phase shift 0according to the rclationship c=sin 0 where c is the ratio of theamplitude of the total energy coupled out of the transmission line atthe junctions and the amplitude of the energy coupled into thetransmission lline at the input thereof.

3. A phase shifter as defined in claim 2 wherein the rectangular stubsections have the same broad dimensions as the main wave guide and thenarrow dimensions vary such that amplitudes of the energy coupled out atthe respective T junctions vary according to the coelicients of abinomial expansion.

4. A phase shifter as defined in claim 2 wherein the rectangular stubsections have the same broad dimen- Well known branched-guide hollowWave guide direc- Y tional coupler, and can be even further improved infrequency response by providing a multiplicity of stubs in a suitablearray, e.g. one in which the coupling is varied according to thecoetlicients of a binomial or Tchbyscheif polynomial expansion. 'I'hephase shifter does not materially affect the power handling capacity ofthe wave guide line, since no reactive elements or dielectric materialis introduced into the main wave guide transmission line section itself.Any amount of phase shift can be achieved by using several double-stubphase shifters in tandem if desired. v l

It should be noted that where the dimensions are given in terms ofwavelengths, the wavelengths are the electrical distances not actualdistances, and a correction for fringing field effects at the junctionsmust be considered, as taught in vol. 10, Radiation Laboratory Series,chapter 6, to get physical distances corresponding to the desiredelectrical distances specified.

Since various changes can be made in the above con struction and manyapparently Widely different embodiments of this invention could be madewithout departingfrom the scope thereof, it is intended that all mattercontained in the above description or shown in the accompanying drawingsshall be interpreted as illustrative and not n a limiting sense.

What is claimed is:

1. A wave guide phase shifter operative over a broad band of frequenciesencompassing a design frequency, said phase shifter comprising a mainrectangular wave guide transmission line, a pair of rectangular waveguide shorted stub sections each joined at one end to the broad wall ofthe main wave guide in a series T junction, the stub sections beingsubstantially an eighth wavelength long at the design frequency asmeasured from the junction end to the shorted end, and the stub sectionsbeing spaced from each other along the main wave guide acenter-to-center distance of substantially a quarter wavelength at thedesign frequency, the stub sections being dimensioned so as to produce atotal coupling coeilicient c related to the desired phase shift -0according to the relationship c=sin 0 where cis the ratio of theamplitude of the total energy coupled out of the transmission line atthe junctions and the amplitude of the energy coupled into thetransmission line at the input thereof.

2. A wave guide phase shifter operative over a broad band of frequenciesencompassing a design frequency, said sions as the main wave guide andthe narrow dimensions vary such that amplitudes of the energy coupledout at the respective T junctions vary according -to the coeicients of aTchebyschet polynominal expansion.

5. A microwave phase shifter operative over a broad band of frequenciesencompassing a design frequency, said phase shifter comprising atransmission line having input and output terminals for the transfer ofmicrowave energy from an energy source to a load, said input terminalsbeing directly connected to said source and said output terminals beingdirectly connected to said load, a pair of stub sections each joined atone end to said transmission line, the stub sections being substantiallyan eighth wavelength long at the design frequency as measured from thejunction end to the other end thereof, and the stub sections beingspaced from each other along the transmission line a center-to-centerdistance of substantially a quarter wavelength at the design frequency,the stub sections being dimensioned and terminated so as to produce atotal coupling coefficient c related to the desired phase shift 0according to the relation c=sin 0 where c is the ratio of the amplitudeof the total energy coupled out of the transmission line at thejunctions and the amplitude of the energy coupled into the transmissionline at the'input thereof.

6. A microwave phase shifter operative over a broad band of frequenciesencompassing a design frequency,

` said phase shifter comprising a transmission line having input andoutput terminals for the transfer of microwave energy from an energysource to a load, said input terminals being directly connected to saidsource and said out put terminals being directly connected to said load,a plurality of stub sections each joined at one end to said transmissionlne, the stub sections being substantially an eighth wavelength long atthe design frequency as measured from the junction end to the other endthereof, and the stub sections being spaced from each other along thetransmisison line a center-to-center distance of substantially a quarterwavelength at the design frequency, the stub sections being dimensionedand terminated so as to produce a total coupling coeiiicient c relatedto the desired phase shift 9 according to the relation c=sin 0 where cis the ratio of the amplitude of the total energy coupled out of thetransmission line at the junctions and the amplitude of the energycoupled into the transmission line at the input thereof.

7. A phase shifter as defined in claim 6 wherein the stub sections aredimensioned and terminated such that the amplitudes of the energycoupled out of the transmission line at the respective junctions varyaccording to the coefficients of a binomial expansion.

7 8. A phase shifter as defined in claim 6 wherein the stub sections aredimensioned and terminated such that the amplitudes of the energycoupled out of the transmission line at the respective junctions varyaccording to the cocicients of a Tchebyschcf polynomial expansion.

References Cited in the file of this patent UNITED STATES PATENTS2,147,807 Alford Feb. 21, 1939 2,155,508 Schelkuno `Apr. 25, 19392,159,648 Alford May 23, 1939 2,540,488 Mumford Feb. 6, 1951 2,561,130McClellan July 17, 1951 8 White Sept. 11, 1951 Kock Oct. 23, 1951 FoxMar. 4, 1952 Lovcridgc Dec. 23, 1952 Reed Feb. 17, 1953 Lines June 9,1953 Cutler Nov. 17, 1953 Warnecke et al Aug. 31, 1954 Pierce May 10,1955 Krutter et al Iune 21, 1955 King ..5 June 19, 1956 FOREIGN PATENTSGreat Britain .1 Apr. 7, 1954

